Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#449 ⋊ C2 |
| Sylow | C53 ⋊ #3277 |
476 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,e^d=eg,h^d=h^52523 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3277, C2×#20286365, #28259265, … |
| maximal normal subgroup of | D53×#3277, C2×#20286365, #28259265, … |
| maximal quotient of | #27375409, #27375519, #27375524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16160);